My Double Integrals!

Calculus Level 4

\[ \large \displaystyle \int_0^{\frac {1}{2} } \int_0^{1-2y} xy \ \mathrm d x \ \mathrm d y \]

If the above integral is in the form of \( \frac {a}{b} \) for coprime positive integers, \(a,b\). Find the value of \(a+b\).

Image Credit: Wikimedia Volume under surface by Oleg Alexandrov
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